Ecological-enactive approaches to cognition aim to explain cognition in terms of the dynamic coupling between agent and environment. Accordingly, cognition of one’s immediate environment (which is sometimes labeled “basic” cognition) depends on enaction and the picking up of affordances. However, ecological-enactive views supposedly fail to account for what is sometimes called “higher” cognition, i.e., cognition about potentially absent targets, which therefore can only be explained by postulating representational content. This challenge levelled against ecological-enactive approaches highlights a putative explanatory gap between (...) basic and higher cognition. In this paper, we examine scientific cognition—a paradigmatic case of higher cognition—and argue that it shares fundamental features with basic cognition, for enaction and affordance selection are central to the scientific enterprise. Our argument focuses on modeling, and on how models promote scientific understanding. We base our argument on a non-representational account of scientific understanding and on the material engagement theory, for models are hereby conceived as material objects designed for scientific engagements. Having done so, we conclude that the explanatory gap is significantly less threatening to the ecological-enactive approach than it might appear. (shrink)

Ecological-enactive approaches to cognition aim to explain cognition in terms of the dynamic coupling between agent and environment. Accordingly, cognition of one’s immediate environment depends on enaction and the picking up of affordances. However, ecological-enactive views supposedly fail to account for what is sometimes called “higher” cognition, i.e., cognition about potentially absent targets, which therefore can only be explained by postulating representational content. This challenge levelled against ecological-enactive approaches highlights a putative explanatory gap between basic and higher cognition. In this (...) paper, we examine scientific cognition—a paradigmatic case of higher cognition—and argue that it shares fundamental features with basic cognition, for enaction and affordance selection are central to the scientific enterprise. Our argument focuses on modeling, and on how models promote scientific understanding. We base our argument on a non-representational account of scientific understanding and on the material engagement theory, for models are hereby conceived as material objects designed for scientific engagements. Having done so, we conclude that the explanatory gap is significantly less threatening to the ecological-enactive approach than it might appear. (shrink)

The basic human ability to treat quantitative information can be divided into two parts. With proto-arithmetical ability, based on the core cognitive abilities for subitizing and estimation, numerosities can be treated in a limited and/or approximate manner. With arithmetical ability, numerosities are processed (counted, operated on) systematically in a discrete, linear, and unbounded manner. In this paper, I study the theory of enculturation as presented by Menary (2015) as a possible explanation of how we make the move from the proto-arithmetical (...) ability to arithmetic proper. I argue that enculturation based on neural reuse provides a theoretically sound and fruitful framework for explaining this development. However, I show that a comprehensive explanation must be based on valid theoretical distinctions and involve several stages in the development of arithmetical knowledge. I provide an account that meets these challenges and thus leads to a better understanding of the subject of enculturation. (shrink)

I identify two reasons for believing in the objectivity of mathematical knowledge: apparent objectivity and applications in science. Focusing on arithmetic, I analyze platonism and cognitive nativism in terms of explaining these two reasons. After establishing that both theories run into difficulties, I present an alternative epistemological account that combines the theoretical frameworks of enculturation and cumulative cultural evolution. I show that this account can explain why arithmetical knowledge appears to be objective and has scientific applications. Finally, I will argue (...) that, while this account is compatible with platonist metaphysics, it does not require postulating mind-independent mathematical objects. (shrink)

Hutto and Myin have proposed an account of radically enactive (or embodied) cognition (REC) as an explanation of cognitive phenomena, one that does not include mental representations or mental content in basic minds. Recently, Zahidi and Myin have presented an account of arithmetical cognition that is consistent with the REC view. In this paper, I first evaluate the feasibility of that account by focusing on the evolutionarily developed proto-arithmetical abilities and whether empirical data on them support the radical enactivist view. (...) I argue that although more research is needed, it is at least possible to develop the REC position consistently with the state-of-the-art empirical research on the development of arithmetical cognition. After this, I move the focus to the question whether the radical enactivist account can explain the objectivity of arithmetical knowledge. Against the realist view suggested by Hutto, I argue that objectivity is best explained through analyzing the way universal proto-arithmetical abilities determine the development of arithmetical cognition. (shrink)

How is knowledge of geometry developed and acquired? This central question in the philosophy of mathematics has received very different answers. Spelke and colleagues argue for a “core cognitivist”, nativist, view according to which geometric cognition is in an important way shaped by genetically determined abilities for shape recognition and orientation. Against the nativist position, Ferreirós and García-Pérez have argued for a “culturalist” account that takes geometric cognition to be fundamentally a culturally developed phenomenon. In this paper, I argue that (...) when understood as moderate versions supported by the state-of-the-art research, the nativist and culturalist views are in fact possible to reconcile. While Ferreirós and García-Pérez present the work of Spelke and colleagues as implying that geometric cognition is genetically determined, I argue that they fail to appreciate the role that Spelke and colleagues see for cultural factors. On this basis, I provide theoretical and terminological clarifications and show that moderate versions of the nativist and culturalist view are in fact consistent with each other. I then propose a unifying theoretical framework for future study that can integrate the two accounts in ontogeny by moving beyond the crude nature (nativism) vs. nurture (culturalism) dichotomy. (shrink)

One main challenge of non-platonist philosophy of mathematics is to account for the apparent objectivity of mathematical knowledge. Cole and Feferman have proposed accounts that aim to explain objectivity through the intersubjectivity of mathematical knowledge. In this paper, focusing on arithmetic, I will argue that these accounts as such cannot explain the apparent objectivity of mathematical knowledge. However, with support from recent progress in the empirical study of the development of arithmetical cognition, a stronger argument can be provided. I will (...) show that since the development of arithmetic is (partly) determined by biologically evolved proto-arithmetical abilities, arithmetical knowledge can be understood as maximally intersubjective. This maximal intersubjectivity, I argue, can lead to the experience of objectivity, thus providing a solution to the problem of reconciling non-platonist philosophy of mathematics with the (apparent) objectivity of mathematical knowledge. (shrink)

Why would we want to develop artificial human-like arithmetical intelligence, when computers already outperform humans in arithmetical calculations? Aside from arithmetic consisting of much more than mere calculations, one suggested reason is that AI research can help us explain the development of human arithmetical cognition. Here I argue that this question needs to be studied already in the context of basic, non-symbolic, numerical cognition. Analyzing recent machine learning research on artificial neural networks, I show how AI studies could potentially shed (...) light on the development of human numerical abilities, from the proto-arithmetical abilities of subitizing and estimating to counting procedures. Although the current results are far from conclusive and much more work is needed, I argue that AI research should be included in the interdisciplinary toolbox when we try to explain the development and character of numerical cognition and arithmetical intelligence. This makes it relevant also for the epistemology of mathematics. (shrink)

Beck presents an outline of the procedure of bootstrapping of integer concepts, with the purpose of explicating the account of Carey. According to that theory, integer concepts are acquired through a process of inductive and analogous reasoning based on the object tracking system, which allows individuating objects in a parallel fashion. Discussing the bootstrapping theory, Beck dismisses what he calls the "deviant-interpretation challenge"—the possibility that the bootstrapped integer sequence does not follow a linear progression after some point—as being general to (...) any account of inductive learning. While the account of Carey and Beck focuses on the OTS, in this paper I want to reconsider the importance of another empirically well-established cognitive core system for treating numerosities, namely the approximate number system. Since the ANS-based account offers a potential alternative for integer concept acquisition, I show that it provides a good reason to revisit the deviant-interpretation challenge. Finally, I will present a hybrid OTS-ANS model as the foundation of integer concept acquisition and the framework of enculturation as a solution to the challenge. (shrink)

In recent years, philosophers have developed accounts of cognitive and affective scaffolding to describe the contribution of environmental resources to the realization of mental abilities. However, an integrative account, which captures scaffolding relations in general terms and across domains, is currently lacking. To close this gap, this paper proposes a pattern theory of scaffolding. According to this theory, the functional and causal role of an environmental resource for an individual agent or a group of agents concerning a mental ability in (...) a situational context can be specified by multiple conditions that a scaffold can satisfy. On this view, scaffolds can be described in terms of patterns of relevance-weighted, gradually satisfied scaffolding conditions. The resulting theory will be applied to cases of mathematical cognition to demonstrate its plausibility and feasibility. The pattern theory of scaffolding, it will be shown, has important implications for research on embodied, embedded, extended, and enactive (4E) cognition. (shrink)

Mathematical cognition is widely regarded as the epitome of the kind of cognition that systematically eludes enactivist treatment. It is the parade example of abstract, disembodied cognition if ever there was one. As it is such an important test case, this paper focuses squarely on what Gallagher has to say about mathematical cognition in Enactivist Interventions. Gallagher explores a number of possible theories that he holds could provide useful fodder for developing an adequate enactivist account of mathematical cognition. Yet if (...) the analyses of this paper prove sound, then some of the central approaches he considers are simply not fit for such service. That said, in the final analysis, if crucial additions and subtractions are made, there is a real chance of fashioning a promising enactivist account of mathematical cognition. (shrink)

Research in evolutionary biology and philosophy of biology and cognition strongly suggests that human organisms modify their environment through active processes of niche construction. Recently, proponents of the free-energy principle and variational active inference have argued that their approach can deepen our understanding of the reciprocal causal relationship between organisms and their niche on various scales. This paper examines the feasibility and scope of variational formalisations and conceptualisations of the organism-niche nexus with a particular focus on the extended active inference (...) account. I will draw a conceptual distinction between selective niche construction, developmental niche construction, and organism-niche coordination dynamics and argue that these notions capture different causal patterns, each of which with a distinct scope. Against this background, I will analyse and discuss the extended active inference account and its strategy to integrate variational active inference with work on extended cognition. The proponents of extended active inference assume that their account can provide an explanation of selective niche construction, developmental niche construction, and organism-niche coordination dynamics. However, my key claim will be that this account has the potential to elucidate the workings of organism-niche coordination dynamics, but does not adequately capture the causal patterns of selective niche construction and developmental niche construction. (shrink)

In the literature on enculturation—the thesis according to which higher cognitive capacities result from transformations in the brain driven by culture—numerical cognition is often cited as an example. A consequence of the enculturation account for numerical cognition is that individuals cannot acquire numerical competence if a symbolic system for numbers is not available in their cultural environment. This poses a problem for the explanation of the historical origins of numerical concepts and symbols. When a numeral system had not been created (...) yet, people did not have the opportunity to acquire number concepts. But, if people did not have number concepts, how could they ever create a symbolic system for numbers? Here I propose an account of the invention of symbolic systems for numbers by anumeric people in the remote past that is compatible with the enculturation thesis. I suggest that symbols for numbers and number concepts may have emerged at the same time through the re-semantification of words whose meanings were originally non-numerical. (shrink)